Some drapery traverse rods have heretofore been made as disclosed in U.S. Pat. No. 3,47O,578 with telescopically adjustable inner and outer hollow rods each having a dovetailed shaped mounting rail along their rear side and a support bracket for engaging the mounting rail to support the rod. The support bracket disclosed in that patent included a rod engaging bracket having a single pair of rail engaging jaws with one jaw adjustable toward and away from the other by means of a threaded fastener to accommodate the different size mounting rails on the inner and outer rods. The rod engaging bracket in that patent was slidably mounted on a wall mounting bracket to adjust the spacing of the rod from the supporting surface and the rod engaging bracket was adapted to be locked in an adjusted position on the mounting bracket by another threaded fastener. This support bracket arrangement not only required manufacture and assembly of a number of parts including the screw fasteners, but also required the use of a screw driver in order to adjust the rod engaging bracket to the rails on the inner and outer rods, and to adjust the rod engaging bracket relative to the mounting bracket.